Details

Time bar (total: 7.3s)

sample58.0ms

Algorithm
intervals
Results
13.0ms126×body320valid
10.0ms536×pre80true
9.0ms280×body80nan
6.0ms91×body160valid
2.0ms11×body640valid
1.0ms28×body80valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.1b
(- (* b b) (* (* 4.0 a) c))
26.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
4.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series301.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0405779
11563685
25002674

prune193.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series455.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
48.0ms
(- (* b b) (* (* 4.0 a) c))
148.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
191.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify118.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06402579
131572332
250012319

prune416.0ms

Filtered
160 candidates to 106 candidates (66.3%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 1 (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c))))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
75×*-un-lft-identity
55×add-sqr-sqrt
35×add-cube-cbrt
27×associate-/l*
20×distribute-lft-out--
18×add-exp-log add-cbrt-cube
10×distribute-rgt-neg-in difference-of-squares
7×pow1 cbrt-undiv div-exp associate-/r*
6×associate-/r/ add-log-exp
5×flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-pow1 sqrt-div associate-*r/ prod-exp clear-num cbrt-unprod
1×sub-neg flip3-+ pow1/2 diff-log pow-prod-down sqrt-prod flip-+
Counts
4 → 136
Calls
4 calls:
5.0ms
(sqrt (* 1 (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
10.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c))))))

series447.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(sqrt (* 1 (- (* b b) (* (* 4.0 a) c))))
48.0ms
(- (* b b) (* (* 4.0 a) c))
150.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
182.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* 1 (- (* b b) (* (* 4.0 a) c))))))

simplify117.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06442492
132832194
250012164

prune424.0ms

Filtered
148 candidates to 105 candidates (70.9%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ 0 (* 4.0 (* a c))))
0.2b
(/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
0.3b
(/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(* (/ (sqrt (+ 0 (* 4.0 (* a c)))) 2.0) (/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
665×times-frac
530×add-sqr-sqrt
482×*-un-lft-identity
286×add-cube-cbrt
239×sqrt-prod
148×associate-*r*
98×distribute-lft-out-- difference-of-squares
54×associate-/l*
49×distribute-rgt-neg-in
32×add-exp-log add-cbrt-cube
22×associate-*l*
16×associate-/r/
13×cbrt-undiv div-exp
12×unswap-sqr
11×div-inv
10×associate-/r*
8×flip3-- flip--
7×pow1
6×prod-exp cbrt-unprod
4×sqrt-div add-log-exp
3×associate-/l/
2×frac-2neg flip3-+ clear-num flip-+
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 502
Calls
4 calls:
3.0ms
(sqrt (+ 0 (* 4.0 (* a c))))
22.0ms
(/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
16.0ms
(/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
86.0ms
(* (/ (sqrt (+ 0 (* 4.0 (* a c)))) 2.0) (/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series1.3s

Counts
4 → 12
Calls
4 calls:
120.0ms
(sqrt (+ 0 (* 4.0 (* a c))))
405.0ms
(/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
404.0ms
(/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
403.0ms
(* (/ (sqrt (+ 0 (* 4.0 (* a c)))) 2.0) (/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify120.0ms

Algorithm
egg-herbie
Counts
514 → 514
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0155211251
1500110701

prune1.2s

Filtered
514 candidates to 258 candidates (50.2%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes84.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02914
13314
23314

end0.0ms

sample1.7s

Algorithm
intervals
Results
411.0ms3716×body320valid
309.0ms16332×pre80true
288.0ms8332×body80nan
212.0ms2939×body160valid
72.0ms474×body640valid
32.0ms871×body80valid